Luton have made their ninth summer signing following the arrival of winger Danny Green.
Notts County have signed Togo international Mawouna Amevor on a two-year deal.
The 31-year-old Sweden international's new deal ties him to the Ligue 1 champions until June 2016.
Ibrahimovic, who joined PSG from AC Milan in July 2012, scored a league-high 30 goals last season to help the club win their first French title since 1994.
The former Barcelona, Ajax and Juventus hitman said after penning his new deal at the Parc des Princes: "I don't see a more ambitious club in Europe than Paris St Germain.
"My wish is that Paris St Germain is my last big club. This club is like me: the dream is never big enough."
PSG president Nasser Al-Khelaifi added: "The desire of Zlatan Ibrahimovic, one of the best players in the world, to leave a long and lasting legacy at Paris Saint-Germain is a very strong sign.
"Together, we share the same ambition, to take the club to the summits of the European game."